ALS-XZ Rule Sudoku: Two Almost Locked Sets, One Elimination

What an almost locked set is

Before the ALS-XZ rule sudoku technique can make any sense, you need the idea of an almost locked set. A locked set is a group of N cells that between them hold exactly N candidates - a naked pair is two cells with two candidates, a naked triple is three cells with three, and so on. An almost locked set, or ALS, is one candidate short of that neatness: N cells holding N plus one candidates between them. The key property is simple but powerful. If you could remove any single candidate value from an ALS, the rest would instantly collapse into a proper locked set, forcing its remaining digits into place. That built-in fragility is exactly what the rule exploits, because it means an ALS is always just one elimination away from resolving completely. Two of these fragile sets, placed correctly, can be played off against each other to force a conclusion that neither could reach alone.

The ALS-XZ rule sudoku setup

The ALS-XZ rule sudoku technique uses two separate almost locked sets, which we can call ALS A and ALS B. They must be linked by two special digits, traditionally named X and Z, and each of those two digits has to appear in both sets. Everything rests on how those shared digits behave across the two groups. X is the restricted common: every cell that contains candidate X in ALS A must be able to see every cell that contains X in ALS B - they share a house, so X cannot be placed in both sets at once. That single restriction is the hinge of the whole method. If ALS A does not take X it loses a candidate and locks; if ALS B does not take X it locks instead. Whatever happens, at least one of the two sets is forced to become a locked set, and both of them can never claim X together. Once you have identified the two ALSs and confirmed their restricted common, the ALS-XZ rule sudoku is most of the way to an elimination.

How Z delivers the elimination

Z is the second shared digit, and it is the one that actually pays out. Because one of the two sets is always forced to lock, one of the two sets must place Z somewhere inside itself - you do not know which set, but you know it happens. Therefore any cell that lies outside both sets, yet can see every Z candidate in both ALS A and ALS B, can never hold Z itself, because one of those Z candidates is guaranteed to be true. That outside cell loses Z from its notes, and that single reliable elimination is the entire reward of the ALS-XZ rule sudoku. Picture ALS A as two cells sharing candidates like 3, 6 and 9, and ALS B as another almost locked set that also carries 6 and 9. Let 6 be the restricted common X and 9 be Z; because at least one set must lock and place a nine, any cell seeing all the nines in both sets simply drops nine. It looks elaborate written out, but on the grid it is two small groups and two shared shapes quietly doing the work.

Practising almost locked sets

The ALS-XZ rule sudoku is one of the most satisfying advanced patterns precisely because it looks like sleight of hand until the moment it clicks. It is also demanding on your candidate marks, so a clean, complete grid is not optional. Shapedoku helps here in a very practical way: the nine distinct shapes make each set easy to see as a unit, and the Notes with smart cleanup keep the two almost locked sets readable while you hunt for X and Z. Reach for Extreme puzzles, where structures this rich actually occur, and give yourself permission to work slowly - naming the candidates in each set, checking that your X really is restricted, and only then looking for the Z victim. Once you have spotted your very first ALS-XZ in the wild and watched a stubborn cell give up its candidate, you will start noticing these paired sets on grids that used to look completely closed.